From time to time, in the prior art, suggestions have been made that closed finite polyhedra made up of saddle shaped polygons spanned by minimal surfaces are possible and M. Burt has, in a book entitled "Spatial Arrangements and Polyhedra With Curved Surfaces and Their Architectural Applications", published by Technion, Haifa, Israel, in November of 1966, described a set of polyhedra. Three of Burt's polyhedra can be used to form unary space filling systems. Some of the others are capable of combinations which provide spans, trusses and other architectural elements.
Others, have in recent years, proposed minimal curved surfaces for use as core structures, such as is taught in the patent to Robb, U.S. Pat. No. 3,227,598; or in walls, as is shown in Hauer, U.S. Pat. No. 3,038,278. Similarly, the patent to Hale, U.S. Pat. No. 3,525,663 teaches a cellular core structure using curved surfaces.
According to the present invention, a plurality of curved surface modules are derived as approximations of surfaces of least area, relative to closed polyogonal perimeters. Each module starts with a non-planar skew polygon. When a minimal surface is bounded by the skew polygon, the result is a saddle like, smooth surface which tends to optimize distribution of stress.
Utilizing the concepts of the present invention, a fundamental set of six primary interrelated curved surface modules has been derived. The set includes an octagonal figure, two hexagonal figures, one of which can be modified into pentagonal shape, and three dodecagonal figures. The included angles between adjacent edges of the polygons tend to be either 90.degree., 120.degree., or 135.degree.. The dihedral angles between intersection planes of the skew polygons are either 125.degree. 16' or 109.degree. 28'. Within these constraints, the edge lengths can be established for a given set of modules.
Sets of modules can be assembled and interconnected to form structures which can enclose space as simple finite polyhedra, or as continuous structures capable of virtually indefinite extension. The structures thus created would include curved space labyrinths having complementary tunnel regions which are identical or congruent. Certain of these spatial configurations are adapted to employ, in addition to the curved surface structural modules, planar, regular polygons.
In yet other embodiments, adapted for use in playground equipment, simple connectors have been devised to couple modules together into appropriate structures. Such techniques include plastic hinged joints as well as hingeable flanged couplers, channel members and the like.
In the preferred embodiment of the present invention, the individual modules will be made from rigid or semi-rigid materials so as to resist both tension and compression loads. A plurality of polygonal units can be arranged so that a single continuous membrane can be substituted for a series of interconnected individual modules in a minimal surface which conforms to the several polygons.
A triangulated skeletal approximation can be derived from each curved surface module. Such an approximation would utilize the teachings of a copending application of the inventor entitled "Minimum Inventory Maximum Diversity Building System," filed Aug. 30, 1971, U.S. Ser. No. 176,220. Such structures would utilize strut members to form the perimeter of the module, and other strut members would be used to triangulate the structure to afford structural rigidity.
In another embodiment, an alternative triangulated approximation can be created from a plurality of planar, triangular elements replacing the skeletal strut members. As is taught in the copending Pearce application, supra, a plane triangular plate would be the full structural equivalent of a skeletal frame of the same shape or outline.
It is, therefore, an object of the present invention to provide a set of minimal surface, polygonal modules that are capable of being assembled into integral, self-supporting structures.
It is an additional object of the invention to provide a family of realted, polygonal modules that can be assembled into novel and challenging play structures.
It is a further object of invention to provide a family of related, polygonal modular shapes that can be utilized as a construction toy.